Related papers: Finite-size effects in response functions of molec…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant…
We investigate the effect of electron-electron interactions on the conductance of quasi one-dimensional systems without potential scattering. For a finite temperature or system length, the short-range interaction is not renormalized to 0,…
A Hamiltonian describing the collective behaviour of N interacting spins can be mapped to a bosonic one employing the Holstein-Primakoff realisation, at the expense of having an infinite series in powers of the boson creation and…
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundaries of one and two-dimensional crystalline materials. The…
We present a method which enables solid-state density functional theory calculations to be applied to systems of almost unlimited size. Computations of physical effects up to the micron length scale but which nevertheless depend on the…
We investigate the locality of electronic interactions in aluminum as a function of smearing/electronic temperature in the context of $\mathcal{O}(N)$ Density Functional Theory calculations. Specifically, we determine the convergence in…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
We carry out an interacting shell-model study of binding energies and spectra in the $sd$-shell nuclei to examine the effect of truncation of the shell-model spaces. Starting with a Hamiltonian defined in a larger space and truncating to…
In this paper, the WKB method is extended to be applicable for conformable Hamiltonian systems where the concept of conformable operator with fractional order $\alpha$ is used. The WKB approximation for the $\alpha$-wavefunction is derived…
Using straightforward linear algebra we derive response operators describing the impact of small perturbations to finite state Markov processes. The results can be used for studying empirically constructed - e.g. from observations or…
We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial…
We report an attempt to calculate energy eigenvalues of large quantum systems by the diagonalization of an effectively truncated Hamiltonian matrix. For this purpose we employ a specific way to systematically make a set of orthogonal states…
Entanglement or modular Hamiltonians play a crucial role in the investigation of correlations in quantum field theories. In particular, in 1+1 space-time dimensions, the spectra of entanglement Hamiltonians of conformal field theories…
We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from…
We review our new method, which might be the most direct and efficient way for approaching the continuum physics from Hamiltonian lattice gauge theory. It consists of solving the eigenvalue equation with a truncation scheme preserving the…
We investigate state feedback and observation for infinite-dimensional linear systems, including a variety of partial differential equations with boundary control and observation. We extend the modulating function approach to…
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the…
We consider a simple atomic two-body bound state system that is overall charge neutral and placed in a static electric and magnetic field, and calculate the magneto-electric response function as a function of frequency. This is done from…
We combine the finite size scaling method with the meshfree spectral method to calculate quantum critical parameters for a given Hamiltonian. The basic idea is to expand the exact wave function in a finite exponential basis set and…